Bulletin of Mathematical Biology最新文献

The landscape of computational modeling in cancer systems biology is diverse, offering a spectrum of models and frameworks, each with its own trade-offs and advantages. Ideally, models are meant to be useful in refining hypotheses, to sharpen experimental procedures and, in the longer run, even for applications in personalized medicine. One of the greatest challenges is to balance model realism and detail with experimental data to eventually produce useful data-driven models. We contribute to this quest by developing a transparent, highly parsimonious, first principle in silico model of a growing avascular tumor. We initially formulate the physiological considerations and the specific model within a stochastic cell-based framework. We next formulate a corresponding mean-field model using partial differential equations which is amenable to mathematical analysis. Despite a few notable differences between the two models, we are in this way able to successfully detail the impact of all parameters in the stability of the growth process and on the eventual tumor fate of the stochastic model. This facilitates the deduction of Bayesian priors for a given situation, but also provides important insights into the underlying mechanism of tumor growth and progression. Although the resulting model framework is relatively simple and transparent, it can still reproduce the full range of known emergent behavior. We identify a novel model instability arising from nutrient starvation and we also discuss additional insight concerning possible model additions and the effects of those. Thanks to the framework's flexibility, such additions can be readily included whenever the relevant data become available.

Behavior change significantly influences the transmission of diseases during outbreaks. To incorporate spontaneous preventive measures, we propose a model that integrates behavior change with disease transmission. The model represents behavior change through an imitation process, wherein players exclusively adopt the behavior associated with higher payoff. We find that relying solely on spontaneous behavior change is insufficient for eradicating the disease. The dynamics of behavior change are contingent on the basic reproduction number $R_a$ corresponding to the scenario where all players adopt non-pharmaceutical interventions (NPIs). When $R_a<1$ , partial adherence to NPIs remains consistently feasible. We can ensure that the disease stays at a low level or maintains minor fluctuations around a lower value by increasing sensitivity to perceived infection. In cases where oscillations occur, a further reduction in the maximum prevalence of infection over a cycle can be achieved by increasing the rate of behavior change. When $R_a>1$ , almost all players consistently adopt NPIs if they are highly sensitive to perceived infection. Further consideration of saturated recovery leads to saddle-node homoclinic and Bogdanov-Takens bifurcations, emphasizing the adverse impact of limited medical resources on controlling the scale of infection. Finally, we parameterize our model with COVID-19 data and Tokyo subway ridership, enabling us to illustrate the disease spread co-evolving with behavior change dynamics. We further demonstrate that an increase in sensitivity to perceived infection can accelerate the peak time and reduce the peak size of infection prevalence in the initial wave.

Many imaging techniques for biological systems-like fixation of cells coupled with fluorescence microscopy-provide sharp spatial resolution in reporting locations of individuals at a single moment in time but also destroy the dynamics they intend to capture. These snapshot observations contain no information about individual trajectories, but still encode information about movement and demographic dynamics, especially when combined with a well-motivated biophysical model. The relationship between spatially evolving populations and single-moment representations of their collective locations is well-established with partial differential equations (PDEs) and their inverse problems. However, experimental data is commonly a set of locations whose number is insufficient to approximate a continuous-in-space PDE solution. Here, motivated by popular subcellular imaging data of gene expression, we embrace the stochastic nature of the data and investigate the mathematical foundations of parametrically inferring demographic rates from snapshots of particles undergoing birth, diffusion, and death in a nuclear or cellular domain. Toward inference, we rigorously derive a connection between individual particle paths and their presentation as a Poisson spatial process. Using this framework, we investigate the properties of the resulting inverse problem and study factors that affect quality of inference. One pervasive feature of this experimental regime is the presence of cell-to-cell heterogeneity. Rather than being a hindrance, we show that cell-to-cell geometric heterogeneity can increase the quality of inference on dynamics for certain parameter regimes. Altogether, the results serve as a basis for more detailed investigations of subcellular spatial patterns of RNA molecules and other stochastically evolving populations that can only be observed for single instants in their time evolution.

Efficient coverage for newly developed vaccines requires knowing which groups of individuals will accept the vaccine immediately and which will take longer to accept or never accept. Of those who may eventually accept the vaccine, there are two main types: success-based learners, basing their decisions on others' satisfaction, and myopic rationalists, attending to their own immediate perceived benefit. We used COVID-19 vaccination data to fit a mechanistic model capturing the distinct effects of the two types on the vaccination progress. We proved the identifiability of the population proportions of each type and estimated that $47\%$ of Americans behaved as myopic rationalists with a high variation across the jurisdictions, from $31\%$ in Mississippi to $76\%$ in Vermont. The proportion was correlated with the vaccination coverage, proportion of votes in favor of Democrats in 2020 presidential election, and education score.

Practical limitations of quality and quantity of data can limit the precision of parameter identification in mathematical models. Model-based experimental design approaches have been developed to minimise parameter uncertainty, but the majority of these approaches have relied on first-order approximations of model sensitivity at a local point in parameter space. Practical identifiability approaches such as profile-likelihood have shown potential for quantifying parameter uncertainty beyond linear approximations. This research presents a genetic algorithm approach to optimise sample timing across various parameterisations of a demonstrative PK-PD model with the goal of aiding experimental design. The optimisation relies on a chosen metric of parameter uncertainty that is based on the profile-likelihood method. Additionally, the approach considers cases where multiple parameter scenarios may require simultaneous optimisation. The genetic algorithm approach was able to locate near-optimal sampling protocols for a wide range of sample number (n = 3-20), and it reduced the parameter variance metric by 33-37% on average. The profile-likelihood metric also correlated well with an existing Monte Carlo-based metric (with a worst-case r > 0.89), while reducing computational cost by an order of magnitude. The combination of the new profile-likelihood metric and the genetic algorithm demonstrate the feasibility of considering the nonlinear nature of models in optimal experimental design at a reasonable computational cost. The outputs of such a process could allow for experimenters to either improve parameter certainty given a fixed number of samples, or reduce sample quantity while retaining the same level of parameter certainty.

Due to the complex interactions between multiple infectious diseases, the spreading of diseases in human bodies can vary when people are exposed to multiple sources of infection at the same time. Typically, there is heterogeneity in individuals' responses to diseases, and the transmission routes of different diseases also vary. Therefore, this paper proposes an SIS disease spreading model with individual heterogeneity and transmission route heterogeneity under the simultaneous action of two competitive infectious diseases. We derive the theoretical epidemic spreading threshold using quenched mean-field theory and perform numerical analysis under the Markovian method. Numerical results confirm the reliability of the theoretical threshold and show the inhibitory effect of the proportion of fully competitive individuals on epidemic spreading. The results also show that the diversity of disease transmission routes promotes disease spreading, and this effect gradually weakens when the epidemic spreading rate is high enough. Finally, we find a negative correlation between the theoretical spreading threshold and the average degree of the network. We demonstrate the practical application of the model by comparing simulation outputs to temporal trends of two competitive infectious diseases, COVID-19 and seasonal influenza in China.

We unify evolutionary dynamics on graphs in strategic uncertainty through a decaying Bayesian update. Our analysis focuses on the Price theorem of selection, which governs replicator(-mutator) dynamics, based on a stratified interaction mechanism and a composite strategy update rule. Our findings suggest that the replication of a certain mutation in a strategy, leading to a shift from competition to cooperation in a well-mixed population, is equivalent to the replication of a strategy in a Bayesian-structured population without any mutation. Likewise, the replication of a strategy in a Bayesian-structured population with a certain mutation, resulting in a move from competition to cooperation, is equivalent to the replication of a strategy in a well-mixed population without any mutation. This equivalence holds when the transition rate from competition to cooperation is equal to the relative strength of selection acting on either competition or cooperation in relation to the selection differential between cooperators and competitors. Our research allows us to identify situations where cooperation is more likely, irrespective of the specific payoff levels. This approach provides new perspectives into the intended purpose of Price's equation, which was initially not designed for this type of analysis.

We demonstrate that the Michaelis-Menten reaction mechanism can be accurately approximated by a linear system when the initial substrate concentration is low. This leads to pseudo-first-order kinetics, simplifying mathematical calculations and experimental analysis. Our proof utilizes a monotonicity property of the system and Kamke's comparison theorem. This linear approximation yields a closed-form solution, enabling accurate modeling and estimation of reaction rate constants even without timescale separation. Building on prior work, we establish that the sufficient condition for the validity of this approximation is $s_0\ll K$ , where $K=k_2/k_1$ is the Van Slyke-Cullen constant. This condition is independent of the initial enzyme concentration. Further, we investigate timescale separation within the linear system, identifying necessary and sufficient conditions and deriving the corresponding reduced one-dimensional equations.

In biology, evolutionary game-theoretical models often arise in which players' strategies impact the state of the environment, driving feedback between strategy and the surroundings. In this case, cooperative interactions can be applied to studying ecological systems, animal or microorganism populations, and cells producing or actively extracting a growth resource from their environment. We consider the framework of eco-evolutionary game theory with replicator dynamics and growth-limiting public goods extracted by population members from some external source. It is known that the two sub-populations of cooperators and defectors can develop spatio-temporal patterns that enable long-term coexistence in the shared environment. To investigate this phenomenon and unveil the mechanisms that sustain cooperation, we analyze two eco-evolutionary models: a well-mixed environment and a heterogeneous model with spatial diffusion. In the latter, we integrate spatial diffusion into replicator dynamics. Our findings reveal rich strategy dynamics, including bistability and bifurcations, in the temporal system and spatial stability, as well as Turing instability, Turing-Hopf bifurcations, and chaos in the diffusion system. The results indicate that effective mechanisms to promote cooperation include increasing the player density, decreasing the relative timescale, controlling the density of initial cooperators, improving the diffusion rate of the public goods, lowering the diffusion rate of the cooperators, and enhancing the payoffs to the cooperators. We provide the conditions for the existence, stability, and occurrence of bifurcations in both systems. Our analysis can be applied to dynamic phenomena in fields as diverse as human decision-making, microorganism growth factors secretion, and group hunting.

The development of autoimmune diseases often takes years before clinical symptoms become detectable. We propose a mathematical model for the immune response during the initial stage of Systemic Lupus Erythematosus which models the process of aberrant apoptosis and activation of macrophages and neutrophils. NETosis is a type of cell death characterised by the release of neutrophil extracellular traps, or NETs, containing material from the neutrophil’s nucleus, in response to a pathogenic stimulus. This process is hypothesised to contribute to the development of autoimmunogenicity in SLE. The aim of this work is to study how NETosis contributes to the establishment of persistent autoantigen production by analysing the steady states and the asymptotic dynamics of the model by numerical experiment.